Probability, Paradox, and the Reasonable Person Principle

tunesmith 10 years ago |

The thing about the value of money being roughly logarithmic sent me on a google exploration where I ended up on a suggested "logarithmic flat tax plan". The gist is, you figure out how many times the poverty rate you make, take the log-base-10, and multiple by some flat constant that is the same for everyone - the result would be your tax rate. Right now in the US that constant would be around 9, assuming the same tax scheme would apply to companies that make billions in profits like Apple and Exxon.

JoachimSchipper 10 years ago | |

So Alice earning 10x poverty pays 9 (somethings), while Bob earning 100x poverty pays 18 (somethings)? Note that poor Carol earning 1x poverty pays nothing. I'd expect Alice to be rather unhappy with this system.

(Also, if someone ever manages to earn 0 in a year, you'll have to give all of the world's wealth to him/her. ;-) )

tunesmith 10 years ago | | |

Alice pays 9% of her $117k income. Bob pays 18% of his $234k income. Those are lower tax rates than the present, so not sure why Alice would be unhappy with it. Carol pays nothing. Floor is the poverty rate, so no one makes infinity.

njonsson 10 years ago | | |

Unless I’m mistaken, if Alice pays 9% of $117,000 (i.e., $10,530), then Bob pays 11.7% of $234,000 (i.e., $27,400).

An 18% tax rate would apply to earners of $1,170,000 (i.e., $210,600 in tax).

The high end would be a 63% tax rate applicable to earners of $117 billion (i.e., $73.71 billion in tax).

tunesmith 10 years ago | | |

Yes, I got 2x and 10x confused, thanks.

doesnotexist 10 years ago |

At first I thought there was a bug in experiment 2b he writes that the sample space should be:

{'BB/?b', 'BB/b?', 'BG/b?', 'GB/?b'}

Because he describes the event as "He is observed at a time when he is accompanied by one of his children, chosen at random."

I thought he also needed to include two more cases:

{'BB/?b', 'BB/b?', 'BG/b?', 'GB/?b', 'GB/g?', 'BG/?g'}

Which again gives us 1/3 probability of both being boys.

but I guess the part that comes after the '/' indicates the observation event.

lbarrow 10 years ago |

Great post, I really enjoyed it. Norvig has a knack for modeling these domains in simple, powerful ways.

hammock 10 years ago |

I've always believed the most common responses to St Petersburg Paradox felt incomplete. The biggest miss is not looking at the other side of the transaction. What's the lowest that the casino offering the game would be willing to charge to play it?

jwmerrill 10 years ago | |

I think the gap between what a person would be willing to pay to play this game and what a casino would be willing to charge is the reason that no one plays it.

tunesmith 10 years ago |

Previously discussed when it was an ipython url instead of a jupyter url: https://news.ycombinator.com/item?id=10327409